Question

$L$ and $M$ are two points with position vectors $2\overline{a}-\overline{b}$ and $a+2\overline{b}$ respectively. The position vector of the point $N$ which divides the line segment $LM$ in the ratio $2:1$ externally is

• A. $3\overline{b}$
• B. $4\overline{b}$
• C. $5\overline{b}$
• D. $3\overline{a}+4\overline{b}$

Answer 1

The correct option is C $5\overline{b}$

Given points are $L$ and $M$ are $2\overline{a}-\overline{b}$ and $\overline{a}-2\overline{b}$,

as $N$ divides in the ratio $2:1$ externally,

$\therefore M$ is the mid point of $L$ and $N$,

$⟹N=2M-L$,

$⟹N=2\overline{a}+4\overline{b}-2\overline{a}+\overline{b}$,

$N=5\overline{b}$